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受破坏者影响的抑郁动态的数学建模与最优控制

Mathematical modeling and optimal control of depression dynamics influenced by saboteurs.

作者信息

Nivetha S, Karthik A, Tandon Abhinav, Ghosh Mini

机构信息

Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai Campus, Chennai, Tamil Nadu, 600 127, India.

Department of Mathematics, Birla Institute of Technology Mesra, Ranchi, Jharkhand, 835215, India.

出版信息

Sci Rep. 2025 Feb 25;15(1):6773. doi: 10.1038/s41598-025-90357-w.

DOI:10.1038/s41598-025-90357-w
PMID:40000731
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC11861278/
Abstract

Depression disorder affects millions globally, characterized by symptoms such as profound sadness, loss of interest in activities, and disruptions in eating and sleeping patterns. Understanding depression within the context of chronic pain is essential for developing effective management and intervention strategies. This study utilizes mathematical modeling to analyze depression trends using empirical data from Spain spanning from 2011 to 2022. Our depression model incorporates distinct compartments for primary and secondary depressed populations, along with a category for individuals categorized as saboteurs, who may actively influence the depression prevalence. We calculated the basic reproduction number [Formula: see text] and identified four equilibrium points and evaluated their stability. Additionally, sensitivity analysis was conducted to assess the impact of [Formula: see text] on depression prevalence. Furthermore, optimal control strategies were explored for the model. These strategies aim to improve treatment adherence, encourage doctor consultations, promote self-medication practices, and enhance recovery rates, ultimately aiming to reduce spread of depressive disorders and associated mortality. Data fitting was conducted using Python, and simulations were carried out in MATLAB to ensure rigorous validation of the model.

摘要

抑郁症在全球影响着数百万人，其特征包括深度悲伤、对活动失去兴趣以及饮食和睡眠模式紊乱等症状。在慢性疼痛的背景下理解抑郁症对于制定有效的管理和干预策略至关重要。本研究利用数学建模，使用西班牙2011年至2022年的实证数据来分析抑郁症趋势。我们的抑郁症模型为原发性和继发性抑郁症人群设立了不同的类别，还有一类被归类为破坏者的个体，他们可能会积极影响抑郁症的患病率。我们计算了基本再生数[公式：见原文]，确定了四个平衡点并评估了它们的稳定性。此外，还进行了敏感性分析以评估[公式：见原文]对抑郁症患病率的影响。此外，还探索了该模型的最优控制策略。这些策略旨在提高治疗依从性、鼓励就医咨询、促进自我用药行为并提高康复率，最终目标是减少抑郁症的传播及相关死亡率。使用Python进行数据拟合，并在MATLAB中进行模拟以确保对模型进行严格验证。

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